Drastic fall-off of the thermal conductivity for disordered lattices in the limit of weak anharmonic interactions

Huveneers, François

Huveneers, François (2013), Drastic fall-off of the thermal conductivity for disordered lattices in the limit of weak anharmonic interactions, Nonlinearity, 26, 3. http://dx.doi.org/10.1088/0951-7715/26/3/837

Type

Article accepté pour publication ou publié

Date

2013

Journal name

Nonlinearity

Volume

Number

Publisher

IOP Publishing

Abstract (EN)

We study the thermal conductivity, at fixed positive temperature, of a disordered lattice of harmonic oscillators, weakly coupled to each other through anharmonic potentials. The interaction is controlled by a small parameter epsilon > 0. We rigorously show, in two slightly different setups, that the conductivity has a non-perturbative origin. This means that it decays to zero faster than any polynomial in epsilon as epsilon → 0. It is then argued that this result extends to a disordered chain studied by Dhar and Lebowitz (2008 Phys. Rev. Lett. 100 134301), and to a classic spin chain recently investigated by Oganesyan, Pal and Huse (2009 Phys. Rev. B 80 115104).

Subjects / Keywords

Condensed matter: structural, mechanical & thermal; Statistical physics and nonlinear systems